Question about complex power in three phase circuits

In summary, the conversation discusses the calculation of complex power absorbed by a combined load consisting of a Y-connected load and a balanced three-phase motor. The line voltage is given as 840 V rms and the power factor of the motor is 0.8 lagging. The correct equation to calculate the complex power of the Y-connected load is S=VI*, not S= (3)^1/2 * Line Voltage * Line Current. This is because the line voltage is the line-to-line or phase-to-phase voltage, while the phase to neutral voltage is equal to the line voltage divided by 1.732. Therefore, dividing the line voltage by the phase to neutral impedance is not a correct expression.
  • #1
kstorm19
4
0

Homework Statement


Assume that the two balanced loads are supplied by an 840-V rms 60-Hz line. Load #1: Y-connected with 30+j40 Ω per phase, Load #2: balanced three-phase motor drawing 48 kW at a power factor of 0.8 lagging. Assuming abc sequence, calculate the complex power absorbed by the combined load.

Both loads are in parallel.

Homework Equations


I= V/Z
S=VI*
S= (3)^1/2 Vl * Il

The Attempt at a Solution


I wanted to specifically know about load 1. To obtain the complex power absorbed by the combined load, I have to calculate the complex power of load 1 and load 2. Load 2 is easy, as I'm already given the power factor and the real power. I'm confused about load 1, however. If this load is in wye, and the voltage I'm being given is the line voltage, then if I divide 840/(30+j40) I will get the line current, right?

So the next thing is finding the complex power. I now have the line voltage and the current voltage, so I attempted to use the equation: S= (3)^1/2 * Line Voltage * Line Current. The result isn't correct as shown by the book answers.

So then I used the equation S=VI* and it gave me the correct answer, which is 14.112 KVA and an angle of 53.13 degrees.

My question is: why can't I use the equation S= (3)^1/2 * Line Voltage * Line Current ? Is there something that I'm missing?

Thank you very much for your time and help.
 
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  • #2
What is the line voltage? In my usage, the line voltage is the line-to-line or phase-to-phase voltage.

The phase to neutral voltage is equal to the line voltage divided by 1.732.

So, dividing a line voltage (840 in your case) by the phase to neutral impedance is not a correct expression. The phase to neutral impedance is seeing the phase to neutral voltage (i.e., 840/1.732).
 
  • #3
magoo said:
What is the line voltage? In my usage, the line voltage is the line-to-line or phase-to-phase voltage.

The phase to neutral voltage is equal to the line voltage divided by 1.732.

So, dividing a line voltage (840 in your case) by the phase to neutral impedance is not a correct expression. The phase to neutral impedance is seeing the phase to neutral voltage (i.e., 840/1.732).

Thank you very much. I've understood now.
 

FAQ: Question about complex power in three phase circuits

What is complex power in a three phase circuit?

Complex power in a three phase circuit is the combination of real power (measured in watts) and reactive power (measured in volt-amperes reactive or VARs). It is a complex quantity that takes into account both the magnitude and phase difference between the voltage and current in a three phase system.

How is complex power calculated in a three phase circuit?

Complex power is calculated using the formula S = P + jQ, where S is the complex power, P is the real power, and Q is the reactive power. The values for P and Q can be found by multiplying the voltage, current, and power factor of each phase and then adding them together.

What is the difference between real power and reactive power in a three phase circuit?

Real power is the actual power that is being consumed or produced by a three phase circuit, and it is measured in watts. Reactive power is the power that is exchanged between the circuit and the source due to the presence of inductors and capacitors, and it is measured in VARs. Real power is used to perform work, while reactive power is necessary for the proper functioning of the circuit.

How does the power factor affect complex power in a three phase circuit?

The power factor is the ratio of real power to apparent power, and it affects the magnitude of complex power in a three phase circuit. A low power factor means that more reactive power is present, which can lead to inefficiency and increased costs. It is important to have a high power factor in order to minimize losses and ensure the efficient use of power.

Can the complex power in a three phase circuit be negative?

Yes, complex power in a three phase circuit can be negative. This means that the circuit is consuming more power than it is producing, which can occur when there is a high amount of reactive power. Negative complex power is also known as leading power, while positive complex power is known as lagging power.

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